Minecraft model transparency glitch in cycles
All you need for a transparent material in cycles is a Transparent node, a Mix node, and some base shader (Diffuse node).

These are the only needed nodes.

The Image Texture node sends the color of the image only to the Diffuse shader, that is very important (more on that in a bit).
The alpha of the image is used as a mask in the Fac socket of the Mix Shader node. That Fac "mixes" the two Shader input sockets, biased on the value in the alpha channel of the image (alpha channel shown below). The Fac socket is expecting a range between 0 and 1, and that is exactly what the alpha channel is. Anywhere that is black (a value of zero) the top socket is used, so transparent; like wise anywhere that is white in the alpha channel (a value of one) the bottom socket is shown, the diffuse node and thus the color in the image.

The Transparent node adds the transparent component to the material. The color of the Transparent node controls how transparent the transparency will be. White (a value of one) is completely transparent, conversely black (a value of zero)  will not be transparent at all, it will render solid black.
This is why you can not plug the image texture in to the transparent node.
Anywhere the image is not pure white will not render transparent if the image is plugged into the transparent node.



This is the alpha (on the left) of image in image texture node in the picture above; and (on the right) the output of the nodes pictured above.



Advanced nodes


Here is a slightly more complicated cycles material. All I'm doing is adding in a glossy component to my material.
Do note though, that even with the extra nodes, it does not change the simple transparency setup.